Effect of gravity modulation on the stability of a horizontal double-diffusive layer

Abstract

The instability characteristics of a horizontal stably stratified fluid layer being heated from below, including its subsequent nonlinear evolution under steady and modulated gravity, have been investigated by experiments and two-dimensional numerical simulations. The critical condition at instability onset is also checked using linear stability analysis. The fluid is contained in a horizontal test tank with an initial stable solute gradient and a constant-temperature gradient imposed by heating from below. Because of the non-diffusive boundaries, the vertical solute gradient slowly decreases and, eventually, the layer becomes unstable. From the time of the onset of instability, the critical solute Rayleigh number is determined. For the experiments with modulated gravity, the tank is fixed onto a platform that oscillates vertically at 1 Hz with an amplitude of 10 cm. The experiment is designed such that no internal wave mode of instability can be excited. The experimental results show that gravity modulation destabilizes the system slightly by increasing the solute Rayleigh number at onset by 8.4% and causes the oscillation frequency at onset to increase by 32.6%. Linear stability analysis and two-dimensional numerical simulations for the steady gravity case yield results that are in good agreement with the experiment. For the gravity modulation case, linear stability results do not show any effect of gravity modulation at the frequency of 1 Hz. Numerical simulation results do show increases in both the onset solute Rayleigh number and the oscillation frequency; however, their values are smaller than those obtained in the experiment. The characteristics of the internal wave mode of instability are explored by numerical simulations of a stably stratified solute fluid layer under gravity modulation. The interference effects between the internal wave mode and double-diffusive mode of instabilities are studied by imposing an adverse temperature gradient on the stratified layer.